Power (watts) is a measure of the rate of energy flow. When you turn on a 60W light bulb, it converts energy from electrical energy to light and heat at a rate of 60 joules per second. Every second that the light bulb is turned on, 60 joules of energy is converted from one form to the other. So the wattage tells you how quickly energy is converted; it measures the rate of energy flow.

I'll try a few examples.

A 1 kW electric heater converts electical energy into heat energy (and a bit of light) at a rate of 1000 joules per second. If you run it for one hour (which is 3600 seconds), you have used 1 kWh (one kilowatt-hour) of energy, which is 3,600,000 joules, or 3600 kJ (kilojoules). Here where I live, 1 kWh (3600 kJ) of electrical energy costs about 25 cents.

So a 1 kW electric heater costs 20 cents per hour to run; it uses energy at a rate of 3600 kJ per hour.

If you have a 100W motor that's 90% efficient, that means it consumes 100 joules of energy for every second that it runs, and converts 90 of those joules into mechanical energy. The remaining 10 joules that it consumes every second are converted into other forms of energy - heat, mainly, and vibration/sound. So it is wasting 10 joules per second (10 watts) of energy.